Open neighbourhood
= Open neighbourhood
{title2=$x\in U\in\mathcal T$}
= Open neighborhood
{synonym}
An <open neighbourhood> of a point $x$ in a <topological space> $(X,\mathcal T)$ is an <open set> $U$ containing $x$. A general <neighbourhood> need only contain an <open neighbourhood>; it need not itself be <open>. A finite <intersection> of <open neighbourhoods> of the same point is again an <open neighbourhood>, by the <topology axioms>.